13. y(4) - 4y"" + 6y" - 4y' + y = 0; y(0) = 0, y'(0) = 1, y"(0) = 0, y""(0) = 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
13please
write clearly
Transcribed Image Text:out explicitly.
2. F(s) =
Problems
In each of Problems 1 through 7, find the inverse Laplace transform
of the given function.
3
1-
1. F(s)
·5² +4
3. F(s) =
4. F(s) =
5. F(s)
=
2
s²+3s-4
2s+2
s² +2s +5
2s - 3
5²-4
8s24s +12
s(s² + 4)
1-2s
s² + 4s +5
In each of Problems 8 through 16, use the Laplace transform to solve
the given initial value problem.
8. y" - y' - 6y=0;
9. y" + 3y' + 2y = 0;
6. F(s) =
M
particular physical systems, but usually we do not point this
FORS
4
(s - 1)³
7. F(s) =
sing
sa
y(0) = 1, y'(0) = -1
y(0) = 1, y'(0) = 0
the gre
bm (2)D IT
vlovinegaen
nl
10.
11.
0 <
y" - 2y' + 2y = 0;
y" - 2y + 4y = 0;
(²₂²2 = {(\)))
y(0) = 0,
y(0) = 2,
y" + 2y' + 5y = 0;
y(0) = 2,
y(4) - 4y + 6y" - 4y + y = 0;
12.
13.
y'(0) = 1, y"(0) = 0, y""(0) = 1
3-
y" + 4y =
18. y" +4y=
14. y(4) - y = 0; y(0) = 1, y'(0) = 0, y"(0) = 1,0 ai al
y'" (0) = 0
15. y"+w²y = cos(2t), w² #4; y(0) = 1, y'(0) = 0
16. y" - 2y + 2y = et; y(0) = 0, y'(0) = 1
In each of Problems 17 through 19, find the Laplace transform Y(s) =
L{y} of the solution of the given initial value problem. A method of
determining the inverse transform is developed in Section 6.3. You
may wish to refer to Problems 16 through 18 in Section 6.1.
17.
y(0) = 1, y'(0) = 0
1, 0≤t< π,
π ≤ t < ∞0;
0,
t,
1,
0≤t< 1,
1≤t < 0;
19. y"+y=2-t,
0,
galwollo) edi madi gnimuzzA
edivihov mai-yd-ombu
y'(0) = 1 IS amaldor
y'(0) = 0motanou oosiqs.)
y'(0) = -1
y(0) = 0,
0 ≤ t < 1,
1≤t < 2,
2 ≤t <∞0;
y(0) = 0, y'(0) = 0
15
y(0) = 0, y'(0) = 0
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